A firm uses capital and labor to produce a single output good. The production function is given by F(K, L) = K L0.5 where K is the amount of capital...

A firm uses capital and labor to produce a single output good. The production function is given by F(K, L) = K L0.5 where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively, r = $6 and w =$5. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decides to limit its total cost to $36,000. Illustrate your solution graphically: draw the relevant isocost line and sketch the relevant isoquant.